Chapter 1 - Investments: Background and Issues

Transcription

1 Chapter 1 - Investments: Background and Issues Investment vs. investments Real assets vs. financial assets Financial markets and the economy Investment process Competitive markets Players in investment markets Recent trends Investments as a profession Investment vs. investments Investment: the commitment of current resources in the expectation of deriving greater resources in the future For example: You cut current consumption to purchase stocks and anticipate that stock prices will rise in the future You forgo current leisure and income to take the investments class and expect that a degree from CSUN will enhance your future career Investments The detailed study of the investment process - focus of this class Real assets vs. financial assets Real assets: assets used to produce goods and services Financial assets: claims on real assets or income generated by real assets Financial assets Fixed-income securities: paying a fixed stream of income over a specified period -CDs, bonds, T-bills, etc Equity: ownership in a corporation - stocks Derivative securities: their payoffs depend on the values of other assets - futures, options, swaps, etc (FIN Futures and Options for more details) Balance sheet for U.S. households, 2008 (Table Digital Image) Real assets: $26,395 billion (37.5%) Liabilities: $14,496 billion (20.6%) Financial assets: $44,071 billion (62.5%) Net worth: $55,970 billion (79.4%) Total $70,466 billion (100%) Total $70,466 billion (100%) 1

2 Financial markets and the economy Informational role of financial markets Consumption timing Allocation of risk Separation of ownership and management: agency problem Corporate governance: accounting scandal, analyst scandal, IPO share allocation Investment process (1) Investment policy: objective, risk-return trade-off (2) Asset allocation: choice of broad asset classes (3) Security selection: choice of particular securities to be held in the portfolio (4) Security analysis: valuation of securities (5) Portfolio construction and analysis: selection of the best portfolio (6) Portfolio rebalancing: adjustment of the portfolio Competitive markets Risk-return trade off: no free lunch rule indicates that assets with higher expected returns entail greater risk Efficient markets: security prices should reflect all the information available in the market quickly and efficiently Players in investment markets Government: federal, state, and local Business: firms and corporations, including financial intermediaries Individuals: individual investors, institutional investors Financial intermediaries: institutions that connect borrowers and lenders such as banks, investment companies, insurance companies, and credit unions, etc Investment bankers: specializing in the sale of new securities to the public in the primary market Primary markets vs. secondary markets Primary markets are markets for new issues of securities Secondary markets are markets for trading previously issued securities 2

3 Recent trends Globalization: integration of global financial markets Securitization: pooling loans into standardized securities Financial engineering: creation of new securities by combining primitive and derivative securities into one composite hybrid (for example, combining stocks and options) or by separating returns on an asset into classes (for example, separating principal from interest payment in a fixed income security) Computer network Investments as a profession Investment bankers Traders and brokers Security analysts and/or CFA (Chartered Financial Analyst) Portfolio managers Financial planners Financial managers ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 2. Intermediate: 9 and 10 3

4 Chapter 2 - Asset Classes and Financial Instruments Money markets Bond markets Equity markets Market indexes Derivative markets Money markets Money markets vs. capital markets Money markets: short-term, highly liquid, and less-risky debt instruments Capital markets: long-term debt and stocks Securities in money markets: T-bills: short-term government securities issued at a discount from face value and returning the face amount at maturity T-bills are issued weekly with initial maturities of 4 weeks, 13 weeks, 26 weeks, and 52 weeks. The minimum denomination is $100, even though $10,000 denominations are more common. It is only subject to federal taxes and is tax exempt from state and local taxes. Bid vs. asked price Bid price is the price you will receive if you sell a T-bill to a dealer Asked price is the price you pay to buy a T-bill from a dealer Asked price > bid price, the difference is called bid-ask spread - profit for a dealer T-bills are quoted in yields based on prices (Figure Digital Image) For example, a 161 day T-bill sells to yield 1.19% means that a dealer is willing to sell the T-bill at a discount of 1.19%*(161/360) = 0.532% from its face value of $10,000, or at $9, [10,000*( ) = 9,946.80]. If an investor buys this T-bill, the return over 161 days will be ($10,000/$9,946.80) - 1 = 0.535%. The annualized return will be 0.535%*(365/161) = 1.213%. Similarly, a dealer is willing to buy the 161 day T-bill at a discount of 1.20% or at $9, for a face value of $10,000. [10,000*( *(161/360)) = $9,946.33] CDs: a bank time deposit Commercial paper: a shot-term unsecured debt issued by large corporations 4

5 Banker s acceptance: an order to a bank by a customer to pay a sum of money in a future date Repurchase agreements (Repos): short-term sales of government securities with an agreement to buy them back later at a higher price Other short-term debts Bond markets T-notes and T-bonds: debt issued by the federal government with original maturity of more than one year. The minimum denomination is $1,000. T-notes: up to 10 years in maturity and pay semiannual interests T-bonds: up to 30 years in maturity and pay semiannual interests Coupon rate and coupon payments Prices are quoted as a percentage of $100 face value (in units of 1/32 of a point) (Figure Digital Image) For example, a quoted price of 96:10 means a price of $ (or $ ) for a face value of $100, or $ for a $1,000 face value bond. Inflation-protected T-bonds (TIPS): the principal amount is adjusted in proportion to increases in the Consumer Price Index to earn a constant stream of income in real dollars Municipal bonds: tax-exempt bonds issued by state and local governments Equivalent taxable yield: r = r m /(1 t) After tax return: r m = r*(1 t) Example: suppose your marginal tax rate is 28%. Would you prefer to earn a 6% taxable return or 4% tax-free yield? What is the equivalent taxable yield of the 4% tax-free yield? Answer: 6%*(1-28%) = 4.32% or 4%/(1-28%) = 5.56% You should prefer 6% taxable return because you get a higher return after tax, ignoring the risk 5

6 Federal agency debt: issued by government agencies, such as Freddie Mac, Fannie Mac, and Ginnie Mac Corporate bonds: issued by corporations (rated from AAA, AA, A, BBB, BB, ) Mortgages and mortgage-backed securities Mortgage lenders originate different loans, including fixed or variable loans and then bundle them in packages and sell them in the secondary market. International bonds Equity markets Common stock: ownership of a corporation Characteristics: residual claim and limited liability Stock market listing for General Electric (Figure Digital Image) Stock Symbol (GE) Close (Closing price is $25.25) Net Change (-$0.43, the change from the closing price on the previous day) Volume (trading volume is 44,302,631 shares) 52 week high and low (range of price, for GE, $ $22.16) Dividend ($1.24 is the annual dividend, or $0.31 last quarter) Dividend yield (1.24/25.25 = 4.9%) P/E (price to earnings ratio is 12) Preferred stock: hybrid security with both bond and common stock features Cumulative and. non-cumulative preferred stocks Tax treatment for firms: 70% of preferred stock dividends received by a firm is tax-exempt (70% exclusion) 70% exclusion doesn t apply to individuals Market indexes Averages vs. indexes Averages: reflect general price behavior in the market using the arithmetic average, price weighted Indexes: reflect general price behavior in the market relative to a base value, market value weighted 6

7 Dow Jones Industrial Average (DJIA): a stock market average made up of 30 high-quality industrial stocks and believed to reflect the overall stock market Current Dow Companies (Table Digital Image) Closing P 1 + Closing P Closing P 30 DJIA = DJIA divisor S&P 500 index: a market value-weighted index made up of 500 big company stocks and believed to reflect the overall market Current closing market value of stocks S&P indexes = Based period closing market value of stocks Market value (market cap) = market price * number of shares outstanding Note: stocks in DJIA and S&P indexes can change Other averages and indexes Dow Jones transportation average (20 transportation stocks, price weighted) Dow Jones utility average (15 utility stocks, price weighted) Dow Jones composite average (65 stocks, including 30 industrial, 20 transportation, and 15 utility stocks, price weighted) NYSE composite index: behavior of stocks listed on the NYSE Nasdaq 100 index: OTC market stock behavior Russell 2000 index: small stock behavior Wilshire 5000 index (NYSE and OTC): overall stock market behavior Market indexes, example 1 You are given the following information regarding stocks X, Y, and Z: Stock price # of shares outstanding Date X* Y Z X* Y Z 0 $50 $50 $

8 * Stock X has a 2-for-1 stock split before trading on day 1. Date 0 is the base date. The current divisor is 3.0 and the base value for an S&P type of index is supposed to be10. Q1. What would be the value of an S&P type index at the end of date 1? 26* * *100 S&P index = x 10 = * * *100 Rate of return on date 1 = (10.27/10) 1 = 2.7% Q2. What would be the value of an S&P type index at the end of date 2? 27* * *100 S&P index = * 10 = * * *100 Rate of return on two days = (10.53/10) 1 = 5.3% Q3. What would be the value of a DJIA type average at the end of date 2? At the end of date 0: DJIA type average = ( ) / 3 = 50 Before date 1: DJIA type average = ( ) / d = 50, solve for d = 2.5 (Rational: A 2-for-1 stock split for stock X will split the price in half but it should not affect the average itself. Therefore, the divisor should be adjusted.) At the end of date 2: DJIA type average = ( ) / 2.5 = 52.4 Rate of return on two days = (52.4 / 50) 1 = 4.8% Market indexes, example 2 Consider a price weighted market average composed of three securities, A, B, and C, with prices of 20, 30 and 40 respectively. The current divisor is What will be the new divisor if stock B issues a 10% stock dividend? Answer: closing average before stock dividend = ( ) / 3.00 = Adjust the price of stock B: 30 / ( ) = (new stock price for B if B issues 10% stock dividend) Calculate the new divisor: ( ) / d = (stock dividend should not affect the closing average) and solve for the new divisor, d =

9 Derivative markets Derivative assets or contingent claims: payoffs depend on the prices of other (underlying) assets Options: the rights to buy or sell an asset at a specified price on or before a specified expiration date (rights) A call option gives the right to buy an asset A put option gives the right to sell an asset Example1 - you buy a March 140 IBM call option at $5.00 Call option: right to buy Stock option: underlying asset is IBM stock Contract size: 100 shares Exercises price: $140 to buy one share of IBM stock Expiration date: the third Friday in March Option premium: $500 Rationale: you expect IBM stock price is going to rise Example 2 - you buy a March 25 Intel put option for $2.00 Put option: right to sell Stock option: underlying asset is Intel stock Contract size: 100 shares Exercises price: $25 to sell one share of Intel stock Expiration date: the third Friday in March Option premium: $200 Rationale: you expect that Intel stock price is going to fall Futures contracts: call for the exchange of certain goods for cash at an arrangedupon price (future s price) at a specified future date (obligations) Example 3 - you buy a June gold futures contract at $1,300 per ounce Commodity futures contract: underlying asset is a commodity Contract size: 100 ounces Futures price: $1,300 per ounce to buy gold Delivery month: June Rationale: you expect gold price is going to rise Example 4 - a farmer sells an October corn futures contract at 475 Commodity futures contract: underlying asset is a commodity Contract size: 5,000 bushels Futures price: $4.75 per bushel to sell corn Delivery month: October Rationale: the farmer wants to lock in the price, hedging 9

10 ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 3. Intermediate: 12, 13, 14, 18, 19, and CFA1 10

11 Chapter 3 - Securities Markets New issues How securities are traded U.S. securities markets Trading costs Margin trading and short sales New issues Recall primary markets and secondary markets Primary markets: for new issues, either IPOs or existing firms issuing new securities (seasoned offerings) IPOs: initial public offerings, shares being sold to the public for the first time Investment banker: firm specializing in the sale of new securities Underwriting: the process of purchase new shares from the issuing firm and resell the shares to the public Prospectus: a document that describes the firm issuing the security and provides the information about the firm Selling process for large new issues: the role of investment bankers Underwriting; Advising; Distributing Best efforts vs. underwritten issues Underwriting syndicate: a group of investment bankers formed by a leading underwriter to spread the financial risk associated with selling new securities Issuing firm (Figure Digital Image) Lead underwriter Underwriting syndicate Investment banker A Investment banker B Investment banker B Individual/Private Investors 11

12 Private placement: new securities are sold directly to a small group of individuals or wealthy investors Initial return of IPOs: very high first day returns all over the world (Figure Digital Image) IPOs in the long run: in general poor performance, especially in next three years (Figure Digital Image) How securities are traded Types of markets Direct search markets: buyers and sellers seek each other directly, which are the least organized markets, for example, a student buys a used car from another student Brokered markets: brokers offer search services for profits/commissions, for example, the real estate market Dealer markets: dealers specializing in particular assets buy and sell them in their own accounts for profits, for example, the over-the-counter (OTC) markets Auction markets: traders converge at one place to buy and sell assets, for example, the New York Stock Exchange (NYSE). Auction markets are the most efficient markets because all traders will get the best price possible. Types of brokers Full service broker vs. discount broker Types of accounts Cash account vs. margin account (without or with borrowing capacity) Bid price - the highest price a dealer is willing to pay for a given security Asked price - the lowest price a dealer is willing to sell a given security Bid-ask spread: the difference of the two prices, which is the profit for a dealer Types of orders: Market order: to buy or sell at the best price available Limit order: to buy at or below a specified price or sell at or above a specified price Stop order (stop-loss order): to sell when price reaches or drops below a specified level or to buy when price reaches or rises above a specified level. It becomes a market order when the stop price is reached. 12

13 Stop-limit order: a combination of stop and limit orders Comparison of a limit order and a stop order (Figure Digital Image) Price falls below the limit Price rises above the limit Buy Limit-buy order Stop-buy order Sell Stop-loss order Limit-sell order Trading mechanics Dealer markets: trade through dealers, for example, in OTC markets Electronic communication networks (ECNs): direct trade over computer network without market makers or dealers Specialist markets: trade through specialists, for example, in NYSE Specialist: a trader who makes a market in the shares of one or more stocks and maintains a fair and orderly market by dealing personally in the market U.S. securities markets Nasdaq: National Association Security Dealers Automated Quotations System Nasdaq stock market: a computer-linked price quotation system for the OTC markets with about 3,200 firms listed for trading NYSE: New York Stock Exchange, the largest exchange in the U.S. with about 2,800 firms listed for trading Block trade: a large transaction in which at least 10,000 shares of stock are bought or sold Program trade: a coordinated purchase or sale of an entire portfolio Settlement: a trade must be settled in 3 working days, called T+3 settlement Trading costs Full service brokers charge more than discount brokers Fixed-commission schedule - small transactions, for example, $7.95 a trade for up to 1,000 shares Negotiated commissions - large transactions (block trade) Explicit vs. implicit cost Commissions are explicit costs while bid-ask spread is an implicit (hidden) cost 13

14 Margin trading and short sales Types of transactions: Long purchase - direct buy Short selling - sale of borrowed securities Margins: Margin trading - borrow money and buy stock to magnify returns by reducing the amount of capital that must be put in by investors Margin requirements - the minimum amount of equity put in by an investor Initial margin - the minimum amount of equity that must be provided by an investor at the time of purchase, 50% minimum Maintenance margin - the minimum amount of equity that must be maintained in the margin account at all time, 25% minimum Margin call - notification of the need to bring additional equity (1) Buying on margin (borrow money and buy stock): Market value of stock - Loan Equity in account Margin = = (1) Market value of stock Market value of stock Buying on margin, example 1 Suppose you bought 100 shares of XYZ at $50.00 per shares in your margin account. The initial margin is 50% and the maintenance margin is 25%. a) At what price, will you receive a margin call? b) If the price drops to $40, what will happen to your account? c) If the price drops to $30, how much money should you provide to retain the minimum margin requirement? a) 100*50 = $5,000 (total cost to purchase 100 shares) Equity = $2,500 (the amount you provide which is 50% of total cost) Loan = $2,500 (the amount you borrow which is 50% of total cost) Let P be the price at which your maintenance margin drops to 25%, using (1), 100*P - 2, = 0.25, solve for P = $ *P If the price drops below $33.33, you will receive a margin call. 14

15 b) If the price drops to $40 > $33.33, your account is restricted but there is no margin call. c) Let X be the amount of money you need to provide to reduce the loan, 100*30 - (2,500 - X) = 0.25, solve for X = $ *30 (2) Short sale on margin (you borrow shares from your broker and sell them now) Rational: you believe the stock is currently overpriced in the market and expect the price will drop in the future. Up-tick (a price that is higher than that of the previous trade) Up-tick rule in short sale: a rule designed to restrict short selling from further driving down the price of a stock that has dropped more than 10% in one day. At that point, short selling would be permitted if the price of the security is above the current national best bid (uptick). It will enable long sellers to stand in the front of the line and sell their shares before any short sellers once the circuit breaker (a 10% drop in one day) is triggered. Value of assets - Loan Equity Margin = = (2) Value of stock owed Loan Short sale on margin, example 2 Suppose you short sell 100 shares of ABC at $100 per share in your margin account. The initial margin is 60% and the maintenance margin is 30%. a) At what price, will you receive a margin call? b) What will happen if the price rises to $110 per share? c) If the price drops to $80 per share after your short sale, what is the return from short sale if the interest charge totals $500? a) 100*100 = $10,000 (short sale proceeds) 10,000*60% = $6,000 (the initial margin you should provide which is 60% of short sale proceeds) Value of assets = $16,000 Let P be the price at which your margin drops to 30%, using (2), 16, *P = 0.30, solve for P = $ *P If the price rises above $ you will receive a margin call. 15

16 b) If the price rises to $110 < $123.08, your account is restricted but you will not receive a margin call. Money made 100*(100-80) c) Rate of return = = = 25% Money invested 6,000 ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 3. Intermediate: 14, 15, 21, and CFA 1, 2, 3 16

17 Chapter 4 - Mutual Funds and Other Investment Companies Investment companies Mutual funds Costs of investing in mutual funds Mutual fund returns Investing in mutual funds Investment companies An investment company is a type of financial intermediary. It sells itself to the public and uses the funds to invest in a portfolio of securities. Mutual funds are investment companies (open-end). Advantages of investing in mutual funds: Economies of scale Professional management Diversification and divisibility Record keeping and administration NAV: the underlying value on a per share basis of a mutual fund It is determined by the closing-bell prices and it varies every day NAV = (market value of assets - liabilities) / number of shares outstanding For example, a mutual fund has $120 million in assets and 5 million of liabilities. If it has 5 million shares outstanding, the net asset value (NAV) is $23 per share. Managed investment companies: open-end vs. closed-end Open-end fund: investors can buy shares from or sell shares back to the fund at NAV (it may involve in purchase or redemption charges), with no limit on the number of shares the fund can issue Closed-end fund: it is traded at prices that can differ from NAV and the number of shares outstanding is fixed Unit investment trust: money pooled from many investors that is invested in a portfolio fixed for the life of the fund Hedge fund: a private investment pool, open to wealthy or institutional investors, that is exempt from SEC regulations Real estate investment trusts (REITs): similar to closed-end funds that invest in real estate or loans secured by real estate 17

18 Mutual funds Mutual funds are common names for open-end investment companies More than 90% of mutual funds are open-end funds Capital gains vs. current income Investment policy: each fund has its policy contained in the fund s prospectus Money market funds: invested in short-term and low-risk instruments Equity funds: mainly invested in stocks, growth funds vs. income funds Balanced funds: a balanced return from fixed income securities and long-term capital gains Bond funds: invested in various bonds, more current income Index funds: mimic market indexes (for example, S&P 500 index) Sector funds: restrict investments in particular sectors (for example, financial service sector) International funds: invested in international stocks Costs of investing in mutual funds Operating expenses: costs to operate the fund, including administrative expenses, ranging from 0.2% to 2.0% Loads: commission charges, sales charges, or redemption charges Front-end load: deduct a % charge from the initial investment (for example, 5%) Low-load fund: less than 3% of front charge Offering price = NAV / (1 load) or NAV = offering price * (1 - load) No-load fund: selling at NAV, or offering price = NAV Back-end load: a commission change on the sale of shares Other fees: for example, 12b-1 fees to cover marketing and distribution costs 18

19 Mutual fund returns Sources of return: dividend income; capital gains distributions; unrealized capital gains NAV 1 NAV 0 + I 1 + G 1 Rate of return = NAV 0 I 1 : income distribution during the period G 1: capital gains distribution during the period Note: All fees are deducted directly from NAV Example on return of a mutual fund, problem 4-21 on page 105 At the start of the year: $200 million in assets with no liabilities and 10 million shares outstanding At the end of the year: dividend income $2 million; no capital gains distribution; fund price rises by 8%, and 1% of 12b-1 fees is charged at the end of the year Answer: NAV 0 = $20 NAV 1 = 20(1.08)*(1-0.01) = $ I 1 = $0.2 and G 1 = Rate of return = = 7.92% Investing in mutual funds Wealth accumulation Diversification Professional management Low cost Speculation and short-term trading Selection process Objectives What a fund offers investment policy Main holdings Load vs. no-load funds Open-end vs. closed-end funds 19

20 Taxation on mutual fund income Turnover ratio: the ratio of the trading activity of a portfolio to the assets of the portfolio Example: see concept check 4.3 Long-term capital gains Short-term capital gains Dividends If it is a retirement account (Roth IRA, regular IRA, 401K or 403B): all taxes are either exempt or deferred Exchange-traded funds (ETFs): offshoots of mutual funds that allow investors to trade index portfolios, for example, Spider (SPDR) for S&P 500, Diamonds (DIA) for Dow Jones Industrial Average, Qubes (QQQQ) for NASDAQ 100 ASSIGNMENTS 1. Concept Checks and Summary 2. Key Terms 3. Intermediate: 11, 12, 13, 21, 22, and 24 20

21 Chapter 5 - Return and Risk Rates of return Risk and risk premium Historical return Inflation and real return Asset allocation Rates of return Components of return: cash dividend and capital gains (or capital losses) Total return ($) = return from cash dividend + return from capital gains (or losses) Total return (%) = dividend yield + capital gain yield Holding period return (HPR): Ending price Beginning price + Cash dividend HPR = Beginning price Example Div = $4 P 0 = $100 P 1 = $ HPR = = = 10% + 4% = 14% Capital gains yield: % change in price, 10% Dividend yield: % return from dividend, 4% Returns over multiple periods Table 5-1: Quarterly cash flows and rates of return of a mutual fund 1 st quarter 2 nd quarter 3 rd quarter 4 th quarter Assets at the start of quarter 1.0 mil 1.2 mil 2.0 mil 0.8 mil Holding period return (HPR) 10.0% 25.0% (20%) 25.0% Total assets before net inflow 1.1 mil 1.5 mil 1.6 mil 1.0 mil Net inflow 0.1 mil 0.5 mil (0.8 mil) 0.0 mil Assets at the end of quarter 1.2 mil 2.0 mil 0.8 mil 1.0 mil 21

22 Arithmetic mean: simple average, the sum of returns in each period divided by the number of periods - best forecast of performance in the future Arithmetic mean = ( ) / 4 = 10% Geometric mean: time-weighted average return (considers compounding) ( )*(1+0.25)*(1-0.2)*(1+0.25) = (1 + r G ) 4 Solve for r G = 8.29% Dollar-weighted average return: internal rate of return for a project Quarter Net cash flow IRR = 4.17% APR (annual percentage rate) vs. EAR (effective annual rate) APR n EAR ( 1 ) 1 n For example, APR = 6%, n = 4 (quarterly compounding), EAR = 6.14% Risk and risk premium Probability distribution: a list of possible outcomes with associated probabilities Expected return: the mean value of the distribution Variance and standard deviation: measure of dispersion around the mean (risk) Example State of the Economy Scenario, s Probability, p(s) HPR, r(s) Boom % Normal % Recession % Expected return = S E( r) p( s) * r( s) = 14% S s1 2 2 Variance = p( s)*[ r( s) E( r)] = 450; s1 Standard deviation = = 21.21% 22

23 Risk premium: expected return in excess of the risk-free rate, an additional return to compensate for taking risk Risk aversion: reluctant to accept risk E E( r p ) r f, where A is the risk aversion coefficient or A ( rp ) r f 1 2 A p 2 p For example, if the risk premium is 8%, the standard deviation is 20%, then the risk aversion coefficient A = 4. The higher the risk aversion is for an investor, the higher the value of A, and the higher the risk premium. Sharpe (reward-to-volatility) measure = S = (more discussions in Chapter 18) E( r p ) r f p = 8% 20% = 0.4 Historical return Using historical data to estimate mean and standard deviation Example: MO Historical returns: summary statistics for the U.S market and the world during (Table Digital Image) Interpretation of the numbers Normal distribution: 68.26% (1 rule), 95.44% (2 rule), and 99.74% (3 rule) % % % mean-2 mean mean+2 Size effect: average returns generally are higher as firm size declines (Figure Digital Image) 23

24 Inflation and real return Nominal interest rate vs. real interest rate r R i (the real rate, r is approximately equal to the nominal rate, R minus the inflation rate, i) R = r + E(i) Nominal interest rate = the real interest rate + expected inflation rate Inflation rate is measured by consumer price index (CPI) U.S. history of interest rates, inflation, and real interest rates (Figure 5.5 and Table Digital Image) Asset allocation Asset allocation: portfolio choice among different investment classes Risky assets vs. risk-free assets All risky assets form a value-weighted risky portfolio, P All risk-free assets form a risk-free asset with a risk-free rate, r f Complete portfolio: a portfolio including risky assets and risk-free assets Complete portfolio s expected return and risk: E ( r ) * c y * E( rp ) (1 y) r f and c y * p Where E(r c ) and c are the expected rate of return and standard deviation for a complete portfolio, E(r p ) and p are the expected rate of return and standard deviation for the risky assets, r f is the return on the risk-free asset, y is the weight on risky-assets, and 1-y is the weight on the risk-free asset. E(r c ) P E(r p ) y = 1.5 r f y = 0.5 CAL p 24

25 The capital allocation line (CAL): a plot of risk-return combinations available by varying portfolio allocation (weights) between the risk-free asset and the risky portfolio Example: E(r p ) = 15%, p = 22%, r f = 7%, y = 50%, then 15% 7% E(r c ) = 11%, c = 11%, the Sharpe measure = S % Challenge: if y = 1.5 what will happen to the complete portfolio? Where is it located on CAL? What is S? What does it mean (y = 1.5)? Risk aversion vs. risk tolerance Passive investment strategy: holding a combination of a well-diversified market portfolio and a risk-free portfolio, assuming all risky assets are fairly priced in the market. Capital market line (CML): a capital allocation line using the market index portfolio as the risky portfolio (more discussions in Chapters 6 and 7) E(r c ) M E(r M ) y = 1.5 r f y = 0.5 CML M ASSIGNMENTS 1. Concept Checks 2. Key Terms 3. Intermediate: 5, 6, 12-16, and CFA

26 Chapters 6&7 - Efficient Diversification, CAPM and APT Diversification and portfolio risk Portfolio construction with two risky assets Modern portfolio theory Beta coefficient Capital asset pricing model (CAPM) Arbitrage pricing theory (APT) Diversification and portfolio risk Risk of holding a single asset: Probability distribution (a revisit) Expected return: E(r) 2 Variance ( ) and standard deviation ( ) % % % Mean or E(r) 2 Mean or E(r) determines the center of the distribution while (or ) determines how wide the distribution is. The large the, the wider the distribution, and the higher the risk. Risk of holding a portfolio: standard deviation of returns of the portfolio As the number of stocks increases in a portfolio, the portfolio s total risk, decreases. It is known as the diversification effect. Portfolio s total risk = firm s specific risk + market risk = Diversifiable risk + non-diversifiable risk = non-systematic risk + systematic risk (Figure Digital Image) p 26

27 p Firm s specific risk Market risk # of securities in a portfolio Portfolio construction with two risky assets Example: portfolio construction with two risky assets State of economy Probability (p) r A r B Recession % -10% Normal % 0% Boom % 30% Estimate the distribution for each stock E(r A ) = 15%, E(r B ) = 6%, 2 A = 4,335 and A = 65.84% (refer to Chapter 5) 2 B = 264 and B = 16.25% (refer to Chapter 5) Estimate the correlation between two risky assets S Covariance: AB p( i)*[ ra ( i) E( ra )]*[ rb ( i) E( rb )] = -1,020 i1 Since AB = ( AB )*( A )*( B ), where AB is called correlation coefficient Correlation coefficient, AB = AB = 1 perfectly and positively; 0 < AB <1 positively but not perfectly; AB = 0 no correlation; -1 < AB < 0 negatively but not perfectly; AB = -1 perfectly and negatively 27

28 r A r A * * * AB = 1 * * AB = -1 * * * r B r B * * * What will the diagrams look like if 0 < AB <1, -1 < AB < 0, and AB = 0? Portfolio s return and risk Three rules for two-risky-assets portfolio (1) The return on a portfolio is a weighted average of the returns on the component securities (A and B), with the investment proportion as weights; r p w A r A w B r B (2) The expected return on a portfolio is a weighted average of the expected returns on the component securities (A and B), with the investment proportion as weights; E( rp ) wae( ra ) wb E( rb ) (3) The variance of the portfolio is given by 2 p ( w ) ( w ) 2( w )( w ) A A 2 B B = ( wa ) ( A ) ( wb ) ( B ) 2( wawb ) AB = ( wa ) ( A ) ( wb ) ( B ) 2( wawb ) A B AB A A B B AB Suppose you invest 10% in stock A and 90% in stock B. What is the expected rate of return of the portfolio? What is the standard deviation of the return of the portfolio? 2 E(r p ) = 6.9%, p = 73.59, and p = 8.58% 28

29 If you compare stock B with the portfolio, what do you find? The portfolio dominates stock B in both risk (lower risk) and return (higher expected return) Let us construct more portfolios by changing weights Portfolio % in A % in B E(r p ), % p, % Plot all the portfolios in a diagram E(r p ) A MVP* B p How to determine the weights for MVP? By choosing the optimal weights you minimize the variance (risk) w B 2 A AB ; and w 2 2 A wb A B 2 AB 1 (for two risky assets) Effect of AB (correlation coefficient), refer to Figure Digital Image E(r p ) AB = -1 A AB = -1 B AB = 1 p 29

30 AB = -1, perfectly negative correlation, perfect diversification AB = 1, perfectly positive correlation, no diversification -1< AB <1, there are benefits to diversification. Where negative correlation is present, there will be even greater diversification benefits. Modern portfolio theory Markowitz mean-variance model (for n risky assets) Efficient portfolio - a portfolio with the highest expected return for a given level of risk or a portfolio with the lowest risk for a given expected return Efficient frontier the set of efficient portfolios MVP minimum variance (risk) portfolio Investment opportunity set: the set of all attainable portfolios, including efficient and inefficient portfolios E(r p ) Efficient set Investment opportunity set MVP Inefficient set p Indifference curves: curves describing investor s preferences for risk and return, or representing a set of combinations of risk and return that provides the same level of satisfaction Nonsatiation: more is preferred to less Risk aversion: most investors are risk-averse Utility: a measure of the level of satisfaction 30

31 E(r p ) I 2 I 1 Favorite A B C D p Mean-variance criterion: investors desire portfolios that lie to the northwest, which means that investors prefer higher return with less risk I 2 is preferred to I 1 because I 2 provides a higher level of satisfaction (lower risk with same return, i.e., A is better than B, or higher return with same risk, i.e., C is better than D) Choosing the optimal portfolio by combining the indifference curves with the efficient set E(r p ) O* p O* is the optimal choice (tangency point) where the utility (satisfaction) is maximized Points to remember: All portfolios on the efficient set are equally good All risky assets with no borrowing or lending opportunities Different investors may have different estimated efficient set Different investors may have different indifference curves 31

32 When there is a risk-free asset in the market and borrowing and lending are allowed Portfolio returns and risk E(r p ) New efficient set CML O* M r f p When a risk-free asset exists, there is a risk a free rate, r f. We can draw a line from r f, which is tangent to the original efficient set at point M. The line is called the Capital Market Line (CML), which becomes the new efficient set. The optimal choice for the investor is point O* because the indifference curve is tangent to the new efficient set (CML) at that point. Capital Market Line (CML) - concepts, formulas, and implication E(r m ) E(r p ) M CML r f E(r m ) - r f m p ( E( rm ) r f E( rp) r f P : It is the Capital Market Line (CML) formula m CML has the risk-free rate as the intercept and the reward-to-variability ratio as the slope 32

33 Two-fund separation theorem - all investors hold a combination of the risk-free asset and a well-diversified market portfolio, which includes all risky assets in the market (market value weighted) Asset allocation line revisited: the risky portfolio actually is a well-diversified market portfolio E(r) E(r m) r f M E(r m) - r f CML m E(r C ) = y*e(r m) + (1-y)*r f Where y is the weight on the market portfolio and (1-y) is the weight on the riskfree asset Rearranging: E(r C ) - r f = y*(e(r m) - r f ) = y*e(r m) y*r f C = y* m For example, given E(r m) = 12%, m = 20%, r f = 5% If y = 60%, E(r C ) = y*e(r m) + (1-y)*r f = 0.6*12% + 0.4*5% = 9.2% C = y* m = 0.6*20% = 12% Beta coefficient A measure of the market risk (systematic risk) for a stock or a portfolio i, m i, m 2 i, m m i m Characteristic line (CL): a regression line used to estimate the beta coefficient The slope of the CL is the estimated beta coefficient for stock i Example: MO 33

34 Single index model Asset returns are related to the returns of a market index Excess return: rate of return in excess of the risk-free rate (R = r - r f ) R zero. i ai i * Rm i, where i is an error term and the average of error terms is R i * i a i i Taking the variance on both sides of the single index model: R m 2 i 2 i 2 m 2 i Total risk = market risk + specific risk = systematic risk + firm s specific risk m is the proportion of total variance attributed to market fluctuations 2 i Example: In a CAPM equilibrium, the risk-free rate is 5% and the expected rate of return on the market is 10% with a standard deviation of 18% ( m = 18%). A common stock i has an expected return of 12% with a standard deviation of 30% ( i = 30%). What percentage of the total risk for stock i is the firm s specific risk? What percentage is due to the market risk? Answer Step 1: Solve for the beta of stock i, using CAPM 12% = 5% + i (10% - 5%), solving for i = 1.4 Step 2: Solve for the firm s specific risk, using the formula above, 900 = (1.4) 2 (18) 2 + 2i, solving for 2i = Step 3: Calculate the percentages, /900 = 29.44% (firm s specific), /900 = 70.56% (market) 34

35 Capital asset pricing model (CAPM) Assumptions: many investors, homogeneous expectations, one-period utility maximization, perfect capital markets, risk-free borrowing and lending, and capital markets in equilibrium It relates the required (expected) return to the market risk, or beta E r ) r [ E( r ) r ] CAPM model ( i f i m f E(r i ) r f Slope = E(r m ) - r f SML i Intercept = risk-free rate Slope = market risk premium SML - the graphical presentation of CAPM Over-and-under valued securities Example: MO Beta of MO is 0.86, if expected return on the market is 12% and the risk free rate is 5%, the required rate of return for MO is 5% *(12% - 5%) = 11.02% Checking the average return over the past 5 years we find that it is 1.22% per month or 14.64% per year (simple interest) The stock s alpha = 14.64% 11.02% = 3.62% (under priced) since the realized return is higher than the CAPM predicts (above the SML) Limitations with CAPM: rely on the market portfolio and expected returns 35

36 Arbitrage pricing theory (APT) An equilibrium model of expected returns with multi-factors Multi-factor model: R i a R R... i i1 m1 i2 m2 ik R mk i For example, firm size, book-to-market ratio, default-risk, etc. Arbitrage: the process of earning risk-free profit by taking the advantage of mispricing in a particular asset Three characteristics for arbitrage 1. No initial investment from pocket 2. No risk 3. Positive return APT model r i r r )... ( r ) f i1 ( 1 rf ) i2 ( 2 f ik k f i Applications Single index model: consider market factor to estimate beta of GM and use CAPM to estimate the required rate of return of GM 1. Collect data (monthly returns of GM, S&P 500 index monthly returns, and monthly T-bill rates from January 1999 to December 2003, 60 observations) 2. Calculate Excess returns of GM and S&P 500 (R = r - r f ) 3. Run the regression: RGM agm GM * Rm i 4. Look for slope = Then use CAPM to estimate the expected return of GM: E( ri ) r f im ( E( rm ) r f ) 6. Assume r f = 4.00%, market risk premium = 5.5%, expected return = 10.82% Two factor model of Merton: consider market factor and interest rate factor to estimate betas and use multifactor model to estimate expected return of GM 1. Collect data 2. Run the regression: Ri ai imrm itb RTB i to estimate betas 3. Use the two-factor model to estimate expected rate of return E r ) r ( E( r ) r ) ( E( r ) r ) ( i f im M f itb TB f 36

37 Assume that the risk-free rate is 4.00%, the expected market risk premium is 6% and the expected interest rate risk premium is 3%. If the market beta of stock i is 1.2 and interest rate beta of the stock is 0.7, the expected return for stock i is E(r i ) = 4% + 1.2*(6%) + 0.7*(3%) = 13.3% Three factor model of Fama and French: considers market factor, size factor, and book-to-market ratio 1. Collect data and run a multifactor regression: ri rf i im * ( rm rf ) HML * rhml SMB * rsmb i to estimate betas for stock i 2. Use three-factor model to estimate expected rate of return for stock i E( ri ) rf im *[ E( rm ) rf ] HML * E( rhml ) SMB * E( rsmb ) 3. Assuming for Dell (using monthly data over the period ), i, M 1.132, HML , and SMB From French s website, r M r f 7.99%, r HML 4.40%, and r SMB 2.94%, then Dell s expected risk premium E ( r Dell ) r 1.132*7.99% *4.40% *2.94% = 6.32% f ASSIGNMENTS Chapter 6 1. Concept Checks 2. Key Terms 3. Intermediate: 8-12 and CFA 1-3 Chapter 7 1. Concept Checks 2. Key Terms 3. Intermediate: 4-7, 17-19, and CFA

38 Chapter 8 - Market Efficiency Random walks and efficient market hypothesis (EMH) Implications of EMH The role of portfolio manager in an efficient market Evidence of market efficiency and anomalies Interpretation of EMH Random walks and efficient market hypothesis (EMH) Random walk: stock price changes are random and unpredictable Efficient market: prices of securities in the market fully and quickly reflect all available information, which means that there is no arbitrage opportunity Figures 8.1 and Digital Image Forms of efficiency: Weak-form efficiency: stock prices already reflect all information contained in the history of past trading Semistrong-form efficiency: stock prices already reflect all publicly available information in the market Strong-form efficiency: stock prices already reflect all relevant information in the market, including inside information Implications of EMH Technical analysis vs. fundamental analysis Technical analysis: research on recurrent and predictable patterns in the market Relative strength: compare the recent performance of a stock with that of the market or other stocks Resistance level: a price level above which it is supposedly unlikely for a stock or stock index to rise Support level: a price level below which it is supposedly unlikely for a stock or stock index to fall Moving averages: 50-day and 200-day moving averages If the market is efficient, what will happen to technical analysis? 38

39 Fundamental analysis: research on determinants of stock value, such as earnings and dividends prospects, expectations of future interest rates, and risk of the firm Active vs. passive portfolio management Active: search for mispriced (overvalued or undervalued) securities, buy and sell often to timing the market Passive: buy and hold a well-diversified portfolio, buy and hold strategy The role of portfolio manager in efficient market Diversification to reduce firm s specific risks Tax consideration for different investors Resource allocation Demand for investment varies with age, tax bracket, risk aversion, and employment, etc., so portfolio managers can tailor portfolios for different investors. Evidence of market efficiency and anomalies Three main issues (1) The magnitude issue: fund managers deal with portfolios worth hundreds of millions. Only one tenth of 1% will be worth a lot. (2) Selection bias: if a manager knows a way to make money for sure, he/she will keep it secret. (3) Lucky event: sometimes, a fund has a superior performance. It can just be a lucky event (bet the right stocks). Weak-form tests: patterns in stock returns Serial correlation test: involves measuring the correlation between stock returns for various lags and the results indicate fairly weak and positive correlation for short-horizon returns and fairly strong and negative correlation for long-horizon returns Momentum effect: the tendency of poorly-performing stocks and well-performing stocks in one period to continue that abnormal pattern in following periods Buying past winners and selling past losers will make abnormal profits Reversal effect: the tendency of poorly performing stocks and well-performing stocks in one period to experience reversals in the following period Implication: short- and intermediate-horizon momentum and long-run reversal 39

40 Semi-strong form tests: market anomalies Anomalies: patterns that seem to contradict the EMH P/E ratio effect: low P/E ratio stocks have earned higher average risk-adjusted returns than high P/E ratio stocks Small-firm effect: small firm stocks have earned higher abnormal returns, primary in January Figure Digital Image Neglected-firm effect: less well-known firm stocks have earned abnormal returns Book-to-market effect : high book-to-market value stocks have earned abnormal returns Figure Digital Image Post-earnings-announcement price effect: stock prices don t reflect new information rapidly Figure Digital Image Strong-form tests: inside information Insiders make superior profits with inside information: the market is not strongform efficient Interpretation of EMH Risk premium or inefficiency? For example, Fama and French s three factor model indicates higher returns are associated with more risks Anomalies or data mining? ASSIGNMENT 1. Concept Checks 2. Key Terms 3. Intermediate: and CFA